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The scaling slope of the anti-symmetric mass gap M of compact U(1)_{2+1} lattice gauge theory is obtained analytically in the Hamiltonian formalism using the plaquette expansion. Based on the first four moments of the Hamiltonian with respect to a one-plaquette mean field state the results demonstrate clear scaling of M at and beyond the transition from strong to weak coupling. The scaling parameters determined agree well with the range of numerical determinations available.

This report describes a technique to optimize the current shaped- charge design procedure as follows. Starting with the desired target to be defeated, a determination of the desired penetration characteristics of the jet would be made. Existing jet penetration theory would then be used to estimate the ideal characteristics of the jet to defeat the given target. Volume II describes the modification and utilization of a two-dimensional finite difference continuum mechanics code utilizing the lagrangian coordinate system to calculate the complete jet formation parameters for any generalized axisymmetric shaped charge. The utilization of this code allows a more detailed study of such phenomena as jet stability, bifurcation on the axis, shear gradients, viscosity, shocks, incipient vaporization, surface tension, and possible other effects. The combined use of both the engineering formulations along with the sophisticated two-dimensional code calculation allows design engineers the versatility to design the most optimum shaped charge for their particular application.

The equations of motion of an arbitrary flexible body in orbit were derived. The model includes the effects of gravity with all its higher harmonics. As a specific example, the motion of a long, slender, uniform beam in circular orbit was modelled. The example considers both the inplane and three dimensional motion of the beam in orbit. In the case of planar motion with only flexible vibrations, the pitch motion is not influenced by the elastic motion of the beam. For large values of the square of the ratio of the structural modal frequency to the orbital angular rate the elastic motion was decoupled from the pitch motion. However, for small values of the ratio and small amplitude pitch motion, the elastic motion was governed by a Hill's 3 term equation. Numerical simulation of the equation indicates the possibilities of instability for very low values of the square of the ratio of the modal frequency to the orbit angular rate. Also numerical simulations of the first order nonlinear equations of motion for a long flexible beam in orbit were performed. The effect of varying the initial conditions and the number of modes was demonstrated.